TY - JOUR

T1 - Bulk and boundary S-matrices for the SU(N) chain

AU - Doikou, Anastasia

AU - Nepomechie, Rafael I.

N1 - Funding Information:
We are grateful to O. Alvarez and L. Mezincescu for valuable discussions. This work was supported in part by the National Science Foundation under Grant PHY-9507829.

PY - 1998/7/22

Y1 - 1998/7/22

N2 - We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish - Reshetikhin by considering also complex "string" solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1,...,N - 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N - 1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N - l) × U(l), as well as a new "duality" symmetry which maps l ↔ N - l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N - 1] the corresponding boundary S-matrices.

AB - We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish - Reshetikhin by considering also complex "string" solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1,...,N - 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N - 1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N - l) × U(l), as well as a new "duality" symmetry which maps l ↔ N - l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N - 1] the corresponding boundary S-matrices.

KW - Bethe ansatz

KW - Boundary S-matrix

KW - Boundary Yang-Baxter equation

KW - Duality

KW - Integrable spin chain

KW - SU(N) R-matrix

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U2 - 10.1016/S0550-3213(98)00239-9

DO - 10.1016/S0550-3213(98)00239-9

M3 - Article

AN - SCOPUS:0032558059

VL - 521

SP - 547

EP - 572

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -